Consider two firms that compete in Cournot oligopoly. They face inverse demand p(Q) = 120−Q where Q = q1 +q2 is the sum of the two firms’ output. The firms can produce this good at a constant marginal cost of 60.

a. Solve for the Cournot equilibrium quantities in the market. What is the equilibrium price?
b. What is the HHI in this market?
c. Suppose the firms merge to form a monopoly and do not realize any cost efficiencies from it. What is the new equilibrium price? What is the change in HHI arising from the merger?
d. Suppose the firms merge to form a monopoly and as a result the new firm is able to produce at a marginal cost of 30. What is the new equilibrium price? What is the change in HHI arising from the merger?
e. Comment on the following statement: "We are seeing an unprecedented increase in the size of firms and the concentration of industries and suggest the government intervene to protect the interests of consumers."

Detailed step=wise solution is given below:

Explanation:

a)

P = 120 - Q = 120 - q1 - q2

MC1 = MC2 = 60

For Firm 1, Total revenue (TR1) = P x q1 = 120q1 - q12 - q1q2

Marginal revenue (MR1) = \partial TR1 / \partial q1 = 120 - 2q1 - q2

Equating MR1 and MC1,

120 - 2q1 - q2 = 60

2q1 + q2 = 60 (1) (Best response, Firm 1)

For Firm 2, Total revenue (TR2) = P x q2 = 120q2 - q1q2 - q22

Marginal revenue (MR2) = \partial TR2 / \partial Q2 = 120 - q1 - 2q2

Equating MR2 and MC2,

120 - q1 - 2q2 = 60

q1 + 2Q2 = 60 (2) (Best response, Firm 2)

Cournot equilibrium is obtained by solving (1) and (2)

2q1 + q2 = 60 (1)

(2) x 2 results in:

2q1 + 4q2 = 120(3)

(3) - (1) results in: 3q2 = 60

q2 = 20

q1 = 60 - 2q2 [From (2)] = 60 - (2 x 20) = 60 - 40 = 20

Q = 20 + 20 = 40

P = 120 - 40 = 80

Market share, firm 1 = q1 / Q = 20 / 40 = 0.5 = 50%

Market share, firm 2 = q2 / Q = 20 / 40 = 0.5 = 50%

(b) HHI Index = (50)2 + (50)2 = 2,500 + 2,500 = 5,000

(c) A monopolist maximizes profit by equating MR with MC.

P = 120 - Q

TR = P x Q = 120Q - Q2

MR = dTR / dQ = 120 - 2Q

Equating MR & MC,

120 - 2Q = 60

2Q = 60

Q = 30

P = 120 - 30 = 90

In a monopoly, HHI = 10,000

Change in HHI = 10,000 - 5,000 = 5,000 (Increase)

(d) When MC = 30, equating MR & MC:

120 - 2Q = 30

2Q = 90

Q = 45

P = 120 - 45 = 75

In a monopoly, HHI = 10,000

Change in HHI = 10,000 - 5,000 = 5,000 (Increase)

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30